What is meant by the internal resistance of a battery?

There is internal resistance in a battery because a battery is not an ideal voltage source. It may be close, but it is not ideal. As a result, analytically, there will be some series resistance, resistance which places a limit on the maximum current that the battery can provide.

While no battery is ideal, most are sufficiently ideal to not require any consideration of the internal resistance. If your circuit is dependent on the internal resistance of a battery, then it is probably not well suited for that application.